Abstract
A tolerance relation θ of a lattice L, i.e., a reflexive and symmetric relation of L which is compatible with join and meet, is called glued if covering blocks of θ have nonempty intersection. For a lattice L with a glued tolerance relation we prove a formula counting the number of elements of L with exactly k lower (upper) covers. Moreover, we prove similar formulas for incidence structures and graphs and we give a new proof of Dilworth's covering theorem.
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Communicated by I. Rival
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Reuter, K. Counting formulas for glued lattices. Order 1, 265–276 (1985). https://doi.org/10.1007/BF00383603
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DOI: https://doi.org/10.1007/BF00383603